SOLUTION: I need help finding the domain of this equation through algebra. The function is: {{{ sqrt(x)/(x^2-9) }}} thank you in advance!

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Question 220503: I need help finding the domain of this equation through algebra.
The function is:

thank you in advance!

Found 2 solutions by rapaljer, jim_thompson5910:
Answer by rapaljer(4671) (Show Source):
You can put this solution on YOUR website!
There are TWO restrictions here. First of all, the denominator must NEVER equal zero, so x cannot equal 3 or -3.

Secondly, because of the , x must be greater than or equal to zero!

Now, take the intersection of these two requirements, and you have all values greater than or equal to zero, except x=3. In interval notation, this would be
[0,3)U (3, inf)

R^2

Dr. Robert J. Rapalje

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Here are some key things to remember:

1) You cannot take the square root of a negative number. So this means that forces to be positive or zero. This means that

2) You cannot divide by zero. So (ie the denominator can't be zero). This means that or (these values would make the denominator equal to zero. Since , we don't need to worry about

Putting 1) and 2) together gets us the domain (in interval notation): [)()

This basically says that the domain is any non-negative number but